It is desirable to make a multilayered sheet from layers of acrylonitrile-methyl acrylate copolymer and an olefin, because these materials have complimentary properties. For example, acrylonitrile-methyl acrylate copolymer has excellent gas barrier properties, clarity, a glossy appearance after thermoforming, and rigidity, provides easy thermoformability to a multilayered coextruded sheet including it, and can be printed on; however, it does not have a substantial moisture barrier, high heat tolerance, or as high a degree of chemical resistance as some other materials, and it does not have Food & Drug Administration (FDA) approval for use in contacting foods. Polypropylene, on the other hand, has moisture barrier properties, chemical resistance, a higher heat tolerance, and FDA approval for contact with food; however, it is extremely difficult to thermoform; there is no gas barrier, and it is difficult to achieve a glossy appearance with it after thermoforming. There is a difference in the tendency to shrink between the acrylonitrile-methyl acrylate copolymer and the polypropylene, and this difference in shrinkage tends to cause delamination of sheets having layers of both these materials with time.